A Bayesian Nonparametric Mixture Measurement Error Model With Application to Spatial Density Estimation Using Mobile Positioning Data With Multi-Accuracy and Multi-Coverage

Abstract

The development of mobile network technologies has made it possible to collect location data of mobile devices through various positioning technologies. The location data can be used to estimate the spatial density of mobile devices, which in turn can be used by mobile service providers to plan for network capacity improvements. The two most prevalent positioning technologies are the assisted global positioning system (AGPS) and cell tower triangulation (CTT) methods. AGPS data provide more accurate location information than CTT data but can cover only a fraction of mobile devices, while CTT data can cover all mobile devices. Motivated by this problem, we propose a Bayesian nonparametric mixture measurement error model to estimate the spatial density function by integrating both noise-free data (i.e., AGPS data) and data contaminated with measurement errors (i.e., CTT data). The proposed model estimates the true latent locations from contaminated data, and the estimated latent locations, combined with noise-free data, are used to infer the model parameters. We model the true density function using a Dirichlet process (DP) mixture model with a bivariate beta distribution for the mixture kernel and a DP prior for the mixing distribution. The use of bivariate beta distributions for the mixture kernel allows the density function to have various shapes with a bounded support. Moreover, the use of a DP prior for the mixing distribution allows the number of mixture components to be determined automatically without being specified in advance. Therefore, the proposed model is very flexible. We demonstrate the effective performance of the proposed model via simulated and real-data examples.

Keywords:

• Bivariate beta distribution
• Data integration
• Dirichlet process
• Location data
• Measurement error

Supplementary Materials

The codes and data for the simulated example in Section 4.1 are available online.

Acknowledgments

The authors thank the editor, associate editor, and referees for reviewing the manuscript and providing valuable comments.

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIT) (No. 2018R1C1B6004511).